Damage evolution and progressive failure mechanism of composite rock mass under static loading
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摘要: 为研究静载作用下复合岩体的力学特性，利用伺服压力试验机进行不同节理角度复合岩体的静力加载试验，对比分析了静力加载后复合岩体的抗压强度、裂纹扩展规律。考虑到岩石材料的非均匀性建立了弹性损伤本构模型，再现不同节理角度复合岩体的渐进损伤演化过程，并给出加载过程中复合岩体的能量耗散特征。结果表明：随着节理倾角增加，复合岩体的抗压强度逐渐减小，在45°时达到最小值为18.0 MPa，随后开始明显增加，在90°时达到最大值为43.0 MPa，复合岩体强度随节理倾角增加整体表现出明显倒U型变化；基于Weibull分布构建了弹性损伤本构模型，通过单轴压缩和巴西劈裂试验结果与模拟计算结果对照验证了开发本构模型的正确性；对于不同节理角度复合岩体，损伤区在煤体侧开始萌生并沿着节理扩大直至破坏，模拟结果与试验结果吻合较好，实现了静载作用下岩石损伤过程的表征；加载过程中应变能在煤体侧开始集中并沿着节理扩大从而形成失稳，展示了能量集中的时空分布特征。Abstract: To study the mechanical characteristics of composite rock mass under static loading, static loading tests of composite rock mass with different joint angles were conducted using a servo pressure testing machine, and the compressive strength and crack propagation of the composite rock mass were compared and analyzed. Taking into account the inhomogeneity of rock materials, an elastic damage constitutive model was established to reproduce the progressive damage evolution process, and the energy dissipation characteristic was presented during loading. The results show that: With the increase of joint inclination angle, the compressive strength of the composite rock mass gradually decreases, reaching a minimum of 18.0 MPa at 45°. Then the compressive strength begins to increase significantly, reaching a maximum of 43.0 MPa at 90°. The strength of the composite rock mass shows a significant inverted U-shape change with the increase of joint inclination angle. An elastic damage constitutive model was established based on Weibull distribution. The constitutive model was verified by comparing the results of uniaxial compression and Brazilian splitting tests with the simulation results. For composite rock masses with different joint angles, the damage zone starts to originate on the coal side and expands along the joints until it fails. The simulation results are in good agreement with the test results, realizing the characterization of the rock damage process under static loading. Strain energy density begins to concentrate on the coal side and expands along the joints, showing the spatio-temporal distribution characteristics of energy concentration.
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Key words:
- static loading /
- composite rock mass /
- damage evolution /
- progressive failure /
- energy evolution
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图 3 静载下复合岩体力学特性
Figure 3. Mechanical properties of composite rock mass under static loading
图 5 复合岩体节理面力学分析
Figure 5. Mechanical analysis of composite rock mass at joint surface
$ \sigma $is normal stress, $ {\sigma _1} $ is maximum principal stress, $ {\sigma _3} $ is minimum principal stress, $ \alpha < {\alpha _1} $is tangential stress, $ {c_{\text{j}}} $ is cohesion, $ {\varphi _{\text{j}}} $ is friction angle, $ {\alpha _1} $,$ {\alpha _3} $ is joint angle
图 6 岩石(煤)弹性模量Weibull分布
Figure 6. Weibull distribution of Young’s modulus of rock (coal)
图 13 静载下复合岩体水平位移
Figure 13. Horizontal displacement of composite rock mass under static loading
图 14 静载下复合岩体损伤演化过程
Figure 14. Damage evolution processes of composite rock mass under static loading
图 15 静载下复合岩体应变能密度分布
Figure 15. Strain energy density of composite rock mass under static loading
表 1 静力加载不同节理角度试样方案
Table 1. Testing results of samples under static loading
Sample Group Angle/(°) R 5 - C 5 - B 5 - R-C1 5 0 R-C2 5 30 R-C3 5 45 R-C4 5 60 R-C5 5 90 Notes: R is rock, C is coal, B is disk specimen, and R-C is composite rock mass. 
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表 2 静力作用下不同节理角度复合岩体试样的试验结果
Table 2. Testing results of composite rock mass at different angles under static loading
Sample Group Angle/(°) σ/MPa R 5 - 40.0 C 5 - 20.0 R-C1 5 0 30.0 R-C2 5 30 25.0 R-C3 5 45 17.0 R-C4 5 60 22.0 R-C5 5 90 42.0 Note: σ is uniaxial compression strength.
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表 3 模拟岩石试样主要参数
Table 3. Main parameters of rock in numerical simulation
Symbol Parameter Potassium feldspar Chlorite Quartz Other Minimum radius Rmin/mm 0.18 0.18 0.18 0.18 Particle size ratio Rrat 1.52 1.52 1.52 1.52 Density ρ/(kg·m−3) 2600 2500 2750 2700 Fraction factor (Particle) μ 0.67 0.4 0.48 0.32 Stiffness ratio kn/ks 1.3 1.5 1.1 2.7 Contact modulus Ec/GPa 9 8 11 7 Cohesive strength (pb) pbcoh/MPa 70 60 80 40 Tensile strength (pb) pbten/MPa 12 10 14 8 Fraction /(°) 35 30 32 33 Normal Stiffness (sj) sjkn 0.9 0.9 0.9 0.9 Shear Stiffness (sj) sjks 0.3 0.3 0.3 0.3 Tensile strength (sj) sjten/MPa 15 17 22 16 Cohesive strength (sj) sjcoh/MPa 65 72 80 60 Fraction (sj) sjθ/(°) 20 20 20 20 Fraction factor (sj) sjμ 0.3 0.3 0.3 0.3
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表 4 煤样数值模型参数
Table 4. Micro-parameters of coal in model
Parameter Amorphous Clay and others Radiusmin/mm 0.18 0.18 Particle size ratio 1.52 1.52 Density ρ/(kg·m−3) 1650 2200 Fraction factor μ 0.3 0.32 Stiffness ratio (kn/ks) 2.82 2.7 Contact modulus Ec (GPa) 8.0 6.0 Cohesive (pb) (pb)
strengthpb_coh (MPa)43 33 Tensile strength (pb)
pb_ten (MPa)27 8 Fraction factor (pb) 1 1 sjkn 0.9 0.9 sjks 0.3 0.3 sjten/MPa 17 16 sjcoh/MPa 60 60 sjθ/(°) 20 20 sjμ 0.4 0.3
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